Abstract
In the paper basic concepts of a new methodology of the fuzzy boundary element method are presented. This article deals with fuzzy-set-valued mappings which are solutions of the fuzzy boundary integral equations. Exact fuzzy solutions of fuzzy boundary integral equations are defined as well as conditional solutions. Computational fuzzy problems and applications are considered in details for boundary potential problems with fuzzy Dirichlet and Neumann type boundary conditions and fuzzy density source functions in a fuzzy domain.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alefeld G., Herzberger J. (1983) Introduction to Interval Computations, Academic Press, New York
Aumann R. J. (1965) Integrals of Set-Valued Functions, J. Math. Anal. Appl. 12, 1â12
Bauch H., Jahn K.U., Oelschlagel, D., Susse, H., Wiebigke, V. (1987) Intervalmathematik, BSG B.G. Teubner Verlagsgeselschaft, Berlin
Brebbia C. A., Dominguez J. (1989) Boundary Elements â An Introductory Course, Comp. Mechanics Publ., Southampton, Boston
Brebbia C., Telles J. C.F., Wrobel L.C. (1984) Boundary Element Techniques â Theory and Applications in Engineering, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo
Buckley J. J. (1992) Solving Fuzzy Equations in Economics and Finance, Fuzzy Sets and Systems 48, 289â296
Buckley J. J. (1992) Solving Fuzzy Equations, Fuzzy Sets and Systems 50, 1â14
Buckley J. J., Qu Y. (1990) Solving Linear and Quadratic Fuzzy Equations, Fuzzy Sets and Systems 38, 43â59
Buckley J. J., Qu Y. (1990) On Using α-Cuts To Evaluate Fuzzy Equations, Fuzzy Sets and Systems 38, 309â312
Buckley J. J., Qu Y. (1991) Solving Fuzzy Equations: A New Solution Concept. Fuzzy Sets and Systems 39, 291â301
Buckley J. J., Qu Y. (1991) Solving Systems of Linear Fuzzy Equations. Fuzzy Sets and Systems 43, 33â43
BurczyĆski T. (1995) Metoda elementĂłw brzegowych, WN-T, Warszawa
Burczyñski T., Skrzypczyk J. (1995) The Fuzzy Boundary Element Method: A New Solution Concept. Proc. of XII Polish Conference on COMPUTER METHODS IN MECHANICS, Warsaw â Zegrze, Poland, 9â13 May, 65â66
BurczyĆski T., Skrzypczyk J. (1996) Stochastic And Fuzzy Aspects Of The Boundary Element Method, International Conference on Uncertain Structures: Analytical, Numer. and Experimental Methods, Cruise Ship in the Western Caribbean, March 3â10
BurczyĆski T., Skrzypczyk J. (1996) The Fuzzy Boundary Element Method: A New Methodology. Sci. Fasc. of Silesian Tech. Univ., ser. Civil Eng. 83, Gliwice, 25â42
BurczyĆski T., Skrzypczyk J. (1997) Fuzzy Aspects of The Boundary Element Method. Engineering Analysis with Boundary Elements, Special Issue: Stochastic Boundary Element Methods 19, 209â216
BurczyĆski T., Skrzypczyk J. (1997) The Boundary Element Method For Fuzzy Systems. Proc. of the IASTED International Conference on Modelling, Simulation and Optimization, Singapore, August 11â14, 24â27
Dubois D., Prade H. (1979) Fuzzy Real Algebra: Some Results. Fuzzy Sets and Systems 2, 327â348
Dubois D., Prade H. (1988) An Approach to Computational Processing of Uncertainty, Plenum Press, New York, London
Felbin C. (1992) Finite Dimensional Fuzzy Normed Linear Space, Fuzzy Sets and Systems 48, 239â248
Guang-Quan Z. (1991) Fuzzy Continuous Function and Its Properties, Fuzzy Sets and Systems 43, 159â171
Kaleva O. (1987) Fuzzy Differential Equations, Fuzzy Sets and Systems 24, 301â317
Kaleva O. (1990) The Cauchy Problem For Fuzzy Differential Equations, Fuzzy Sets and Systems 35, 389â396
Mikhlin S.G. (1986) Singular Integral Operators, Akademie-Verlag, Berlin
Moore R.E. (1966) Interval Analysis, Prentice Hall, Englewood Cliffs
Nanda S. (1989) On Integration of Fuzzy Mappings, Fuzzy Sets and Systems 32, 95â101
Negoita C.V., Ralescu D.A. (1975) Applications of Fuzzy Sets to System Analysis, Ed. Technica, Birkhauser Verlag, Basel und Stuttgart
Neumaier A. (1990) Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, New York, Port Chester, Melbourne, Sydney
Nguyen H. T. (1978) A Note on the Extension Principle for Fuzzy Sets, J. of Math. Anal. Appl. 64, 369â380
Shary S. P. (1996) Algebraic Approach to the Interval Linear Static Identification, Tolerance, and Control problems, or One more Application of Kaucher Arithmetic, Reliable Comp. 2, 3â33
Skrzypczyk J. (1996) On Fuzzy Singular Integration. Sci. Fasc. of Silesian Tech. Univ. ser. Civil Eng. 83, Gliwice, 121â130
Skrzypczyk J. (1997) Zadanie brzegowe teorii potencja3u w obszarze rozmytym. MateriaĆy Konferencji naukowej z okazji 70-lecia urodzin JĂłzefa GĆomba pt. Wybrane problemy naukowo â badawcze mostownictwa i budownictwa, Gliwice 17 czerwca 1997, Wyd. Politechniki ĆlÄ skiej, Gliwice, 243â251
Skrzypczyk J., BurczyĆski T. (1997) The Fuzzy Boundary Element Method. Proc. of XIII Polish Conference on COMPUTER METHODS IN MECHANICS, Vol. 4, PoznaĆ, Poland, 5â8 May, 1195â1202
Skrzypczyk J., BurczyĆski T. (1997) Fuzzy Aspects of The Boundary Element Method in Elastostatics. Proc. of XXXVI Sympozjon âModelowanie w Mechaniceâ, Wisla 16â20 luty 1997, Zeszyty Naukowe Katedry Mechaniki Stosowanej 3, 25â30
Skrzypczyk J., BurczyĆski T. (1998) Metoda elementĂłw brzegowych dla obszarĂłw o ksztaĆcie rozmytym, MateriaĆy XXVII Sympozjonu âModelowanie w Mechaniceâ, WisĆa 9â13 lutego 1998, Zeszyty Naukowe Katedry Mechaniki Stosowanej 6, 317â322.
Skrzypczyk J., BurczyĆski T. (1998) Fuzzy Boundary Element Method in the Analysis of Uncertain Systems, J. of Theoretical and Applied Mechanics 36, 493â512
Skrzypczyk J., BurczyĆski T. (1998) Boundary Element Methods For Fuzzy Domain, Proc. of IABEM International Symposium on Boundary Element Methods, Ecole Polytechnique, Palaiseau (Paris), France, May 26â29
Skrzypczyk J., Witek H. (2000) Solution Interpretation in Fuzzy Boundary Problems â New Concepts, Proc. of XXXVI Sympozjon âModelowanie w Mechaniceâ, WisĆa 14â18 luty 2000, Zeszyty Naukowe Katedry Mechaniki Stosowanej, 285â288
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Skrzypczyk, J., BurczyĆski, T. (2001). Theoretical and Computational Aspects of the Fuzzy Boundary Element Methods. In: Burczynski, T. (eds) IUTAM/IACM/IABEM Symposium on Advanced Mathematical and Computational Mechanics Aspects of the Boundary Element Method. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9793-7_30
Download citation
DOI: https://doi.org/10.1007/978-94-015-9793-7_30
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5737-2
Online ISBN: 978-94-015-9793-7
eBook Packages: Springer Book Archive